Duality results in Banach and quasi-Banach spaces of homogeneous polynomials and application

Author(s)

Favaro, Vinicius V. ^[1] ; Pellegrino, Daniel ^[2]

Affiliation

^[1] Univ Fed Uberlandia, Fac Matemat, BR-38400902 Uberlandia, MG - Brazil

^[2] Univ Fed Paraiba, Dept Matemat, BR-58051990 Joao Pessoa, PB - Brazil

• Document type: Journal article
• Source: STUDIA MATHEMATICA; v. 240, n. 2, p. 123-145, 2018.
• Web of Science Citations: 1

Abstract

Spaces of homogeneous polynomials on a Banach space are frequently equipped with quasi-norms instead of norms. In this paper we extend a technique to replace the original quasi-norm by a norm in a dual preserving way, in the sense that the dual of the space with the new norm coincides with the dual of the space with the original quasi-norm. Applications to problems on the existence and approximation of solutions of convolution equations and on hypercyclic convolution operators on spaces of entire functions are provided. (AU)

• FAPESP's process: 14/50536-7 - Spaces of holomorphic functions defined on Banach spaces and the Michael’s problem
• Grantee: Vinícius Vieira Fávaro
• Support Opportunities: Scholarships in Brazil - Post-Doctoral